Not applicable.
Not applicable.
The present invention relates to methods for producing free form structures in general, and more particularly to methods for assembling free form three dimensional objects from sheet material.
Computer Aided Design (CAD) software enables a designer to create mathematical models of objects or structures which can be readily viewed on a display, modified, and analyzed. Modem CAD software gives a designer the ability to create any shape imaginable. These models, which are not limited to elemental shapes such as cubes and spheres, are known as free form models, and give free rein to the imagination of the designer and the specific requirements of the project. The appearance of the free form model is clearly and accurately displayed at any desired magnification on a video display.
Generation of actual three-dimensional output objects from the free form CAD source models presents a challenge. If the object is ready for production, the CAD source model can be used to create cutting paths for a multi-axis milling machine which can produce the free form object as a machined part, or a mold can be produced for generating the part in a polymer material.
If the output object is relatively small (usually smaller than a cube two feet on a side), it may be produced by stereolithography, selective laser sintering, or other similar technique which builds up an object or a mold for the object from a series of layers. Various approaches are set out in Automated Fabrication, Marshall Burns, (PTR Prentice Hall, 1993). These techniques, however, are limited in the size of object which can be produced, in the materials used, and generally require costly equipment to implement. These options are costly, and may not be economically employed for custom or large scale objects.
Some source models are especially suited to being constructed from sheets of material. For example, if the model is comprised entirely of planar shapes, it might be assembled from sheets of cardboard or plywood cut to shape and fastened together. More complex shapes can be produced in this manner if the sheet material is capable of being bent. For example, a cylinder is readily constructed from a bent thin sheet. Surfaces which can be produced by bending or folding a sheet, but without stretching, are known as developable surfaces. If the designer employs a CAD program which is constrained to produce models using only developable surfaces, such as disclosed in my U.S. Pat. No. 6,493,603, the disclosure of which is incorporated by reference herein, the developable surfaces of the three-dimensional source model may be flattened, cut out from sheet material, and assembled into a corresponding output object. However, this approach requires modified CAD software, and undesirably places limits on the designer from the beginning of the design creation.
Gershon Elber, of the Department of Computer Science, Technion, Israel Institute of Technology, has described a software approach which decomposes a free form three-dimensional model into piecewise developable surfaces. In this system, a sphere, for example, can be rendered as a series of narrow strips which can be cut from sheets and assembled into an approximation of the sphere. What is needed however, is a system for producing free form three-dimensional structures out of sheet materials formed into developable surface elements, and yet which would provide optimal design latitude to the designer, would minimize the number of elements required, and would offer a range of readily selected creative options to the designer in controlling the conversion of the free form model into the developable surface output object.
The process of this invention produces instructions for forming a three-dimensional object which can be assembled from planar elements of sheet material. The elements are determined such that, when they are assembled, the element surfaces are exclusively developable surfaces. The process begins with a free form source model which may have sharp edges and doubly curved surfaces, as well as developable surfaces. The free form source model is divided into surface sections by identifying external boundary edges and internal boundary edges. Boundary edges may be determined, for example, where surface normals between two adjacent surfaces differ by some selected tolerance, or where a surface is abruptly terminated. The boundaries are connected or further divided as necessary to achieve a perimeter about each surface section which is a single closed curve. Doubly curved surfaces may also be subdivided. Each surface section perimeter is sampled and represented as a series of vertices in three-space connected by edge segments to create a perimeter polygon. A developable output surface which approximates each source model surface section is then determined by calculating the minimum cost triangulation of the perimeter polygon of each surface section. The cost of each triangulation is determined by using functions which either relate the triangles of the triangulation to each other, or to some attribute of the source model surface section, or relate to an innate attribute of the triangles. The function or functions used to assign costs to the triangulations are selected to determine a triangulation which is most satisfactory in terms of the end result desired. A number of factors may be considered as costs to be minimized, including the deviation of the triangle normal from the surface normal at the perimeter, the degree of bending between adjacent triangles, and the departure of the triangulated surface from the original source model surface section. The minimum cost triangulation is carried out as a process which may be assisted by dynamic programming methods. Once the minimum cost triangulation has been determined for each output surface, the triangulated surface is flattened and the two-dimensional boundary is determined. This output surface boundary may be provided as instructions to a cutting tool, or as printed outlines on planar sheet material which thereby permits the output segments to be cut from the sheet material and assembled into an output object comprised entirely of developable surfaces.
It is a feature of this invention to provide a method for producing three-dimensional objects formed entirely of developable surfaces which approximate a source model surface.
It is another feature of this invention to provide a method for approximating a doubly curved surface with two or more developable surfaces.
It is a further feature of this invention to provide a method of forming planar structural material into shapes which approximate free form surfaces.
It is also a feature of this invention to provide a method of dividing doubly curved surfaces into developable surfaces along arbitrary subdividing lines entered by a user.
Further objects, features and advantages of the invention will be apparent from the following detailed description when taken in conjunction with the accompanying drawings.